www.iap.uni-jena.de

Optical Design with Zemax

for PhD - Basics

Lecture 9: Imaging

2020-01-08

Herbert Gross

Speaker: Dennis Ochse

Winter term 2019

Preliminary Schedule

No Date Subject Detailed content

1 23.10. Introduction

Zemax interface, menus, file handling, system description, editors, preferences, updates,

system reports, coordinate systems, aperture, field, wavelength, layouts, diameters, stop

and pupil, solves

2 30.10.Basic Zemax

handling

Raytrace, ray fans, paraxial optics, surface types, quick focus, catalogs, vignetting,

footprints, system insertion, scaling, component reversal

3 06.11.Properties of optical

systems

aspheres, gradient media, gratings and diffractive surfaces, special types of surfaces,

telecentricity, ray aiming, afocal systems

4 13.11. Aberrations I representations, spot, Seidel, transverse aberration curves, Zernike wave aberrations

5 20.11. Aberrations II Point spread function and transfer function

6 27.11. Optimization I algorithms, merit function, variables, pick up’s

7 04.12. Optimization II methodology, correction process, special requirements, examples

8 11.12. Advanced handling slider, universal plot, I/O of data, material index fit, multi configuration, macro language

9 08.01. Imaging Fourier imaging, geometrical images

10 15.01. Correction I Symmetry, field flattening, color correction

11 22.01. Correction II Higher orders, aspheres, freeforms, miscellaneous

12 29.01. Tolerancing I Practical tolerancing, sensitivity

13 19.02. Tolerancing II Adjustment, thermal loading, ghosts

14 26.02. Illumination I Photometry, light sources, non-sequential raytrace, homogenization, simple examples

15 04.03. Illumination II Examples, special components

16 11.03. Physical modeling I Gaussian beams, Gauss-Schell beams, general propagation, POP

17 18.03. Physical modeling II Polarization, Jones matrix, Stokes, propagation, birefringence, components

18 25.03. Physical modeling III Coatings, Fresnel formulas, matrix algorithm, types of coatings

19 01.04. Physical modeling IVScattering and straylight, PSD, calculation schemes, volume scattering, biomedical

applications

20 08.04. Additional topicsAdaptive optics, stock lens matching, index fit, Macro language, coupling Zemax-Matlab /

Python

2

1. Fourier imaging

2. Coherence and imaging

3. Phase imaging

4. Imaging with ZEMAX

Content

3

diffracted ray

direction

object

structure

g = 1 /

/ g

k

kx

▪ Phase space with spatial coordinate x and

1. angle

2. spatial frequency in mm-1

3. transverse wavenumber kx

▪ Fourier spectrum

corresponds to a plane wave expansion

▪ Diffraction at a grating with period g:

deviation angle of first diffraction order varies linear with = 1/g

sin 𝜃𝑥 = 𝜆 ⋅ 𝑣𝑥 =𝑘𝑥𝑘

),(ˆ),( yxEFvvA yx

( ) ( )A k k z E x y z e dx dyx y

i xk ykx y, , ( , , )− +

vk 2

vg

1

sin

Fourier imagingDefinitions of Fourier optics

4

▪ Diffraction of the illumination wave at the object structure

▪ Occurrence of the diffraction orders in the pupil

▪ Image generation by constructive interference of the supported orders

▪ Object details with high spatial frequency are blocked by the system aperture and cannot

be resolved

-1

1

object planesource

pupil plane

image plane

0

imaginglens

Ref: W. Singer

Fourier imagingAbbe theory of microscopic resolution

5

▪ Grating object pupil

▪ Imaging with NA = 0.8

▪ Imaging with NA = 1.3

Ref: L. Wenke

6Fourier imagingResolution and spatial frequencies

▪ Arbitrary object expanded into a spatial

frequency spectrum by Fourier

transform

▪ Every frequency component is

considered separately

▪ To resolve a spatial detail, at least

two orders must be supported by the

system

𝑔 ⋅ sin 𝜃 = 𝑚 ⋅ 𝜆

𝑔𝑚𝑖𝑛 =𝜆

sin 𝜃=

𝜆

𝑁𝐴

Ref: M. Kempe

optical

system

object

diffracted orders

a)

resolved

b) not

resolved

+1.

+1.

+2.

+2.

0.

-2.

-1.

0.

-2.

-1.

incident

light

7Fourier imagingGrating diffraction and resolution

optical

system

object

diffracted orders

a)

resolved

b) not

resolved

+1.

+1.

+2.

+2.

0.

-2.

-1.

0.

-2.

-1.

incident

light

c) off-axis

illumination

+1.

+2.

0.

-1.

-2.

𝑔𝑚𝑖𝑛 =𝜆

2 ⋅ 𝑁𝐴

▪ A structure of the object is resolved, if the first diffraction order is propagated

through the optical imaging system

▪ The fidelity of the image increases with the number of propagated diffracted orders

0. / +1. / -1. order

0. / +1. / -1.

+2. / -2.

order

0. / +1. -1. / +2. /

-2. / +3. / -3.

order

Fourier imagingNumber of supported orders

8

Ref: D.Aronstein / J. Bentley

object

pointlow spatial

frequencies

high spatial

frequencies

high spatial

frequencies

numerical aperture

resolved

frequencies

object

object detail

decomposition

of Fourier

components

(sin waves)

image for

low NA

image for

high NA

object

sum

Fourier imagingResolution of Fourier components

9

▪ Imaging of a crossed grating object

▪ Spatial frequency filtering by a slit:

▪ Case 1:

- pupil open

- Cross grating imaged

▪ Case 2:

- truncation of the pupil by a split

- only one direction of the grating is

resolved

pupil complete open

pupil truncated by slit

image

Fourier imagingFourier filtering

10

▪ Improved resolution by oblique illumination in microscopy

▪ Enhancement only in one direction

centered illumination:

supported orders in y : 0 , +1 , -1

oblique illumination :

supported orders in y : 0 , +1 , + 2

0th order y

1st order in y

2nd order in y

- 1st order in y

no change

in x direction

Fourier imagingOblique illumination in microscopy

11

▪ Optical system with magnification m

Pupil function P,

Pupil coordinates xp,yp

▪ PSF is Fourier transform

of the pupil function

(scaled coordinates)

( )( ) ( )

−+−−

pp

myyymxxxz

ik

pppsf dydxeyxPNyxyxgpp ''

,)',',,(

( ) pppsf yxPFNyxg ,ˆ),(

object

planeimage

plane

source

point

point

image

distribution

Coherence and imagingPoint spread function

12

objectintensity image

intensity

single

psf

object

planeimage

plane

▪ Transfer of an extended

object distribution Iobj(x,y)

▪ In the case of shift invariance

(isoplanatism):

incoherent convolution

▪ Intensities are additive

▪ In frequency space:

- product of spectra

- linear transfer theory

- spectrum of the psf works as

low pass filter onto the object

spectrum

- Optical transfer function

),(*),()','( yxIyxIyxI objpsfima

dydxyxIyyxxIyxI objpsfima

−

−

),()',,',()','(

dydxyxIyyxxIyxI objpsfima

−

−

−− ),()','()','(

),(),( yxIFTvvH PSFyxotf

),(),(),( yxobjyxotfyximage vvIvvHvvI

Coherence and imagingFourier theory of incoherent image formation

13

▪ Transfer of an extended

object distribution Eobj(x,y)

▪ In the case of shift invariance

(isoplanasie):

coherent convolution of fields

▪ Complex fields additive

▪ In frequency space:

- product of spectra

- linear transfer theory with fields

- spectrum of the psf works as

low pass filter onto the object

spectrum

- Coherent optical transfer

function

object

plane image

plane

object

amplitude

distribution

single point

image

image

amplitude

distribution

𝐸𝑖𝑚𝑎(𝑥′, 𝑦′) = න𝐴𝑝𝑠𝑓 𝑥, 𝑦, 𝑥′, 𝑦′ ⋅ 𝐸(𝑥, 𝑦)𝑑𝑥𝑑𝑦

𝐸𝑖𝑚𝑎(𝑥′, 𝑦′) = න𝐴𝑝𝑠𝑓 𝑥 − 𝑥′, 𝑦 − 𝑦′ ⋅ 𝐸𝑜𝑏𝑗(𝑥, 𝑦)𝑑𝑥𝑑𝑦

𝐸𝑖𝑚𝑎(𝑥′, 𝑦′) = 𝐴𝑝𝑠𝑓 𝑥, 𝑦 ∗ 𝐸𝑜𝑏𝑗(𝑥, 𝑦)

𝐻𝑐𝑡𝑓(𝑣𝑥, 𝑣𝑦) = 𝐹𝑇 𝐴𝑝𝑠𝑓(𝑥, 𝑦)

𝐸𝑖𝑚𝑎(𝑣𝑥, 𝑣𝑦) = 𝐻𝑐𝑡𝑓(𝑣𝑥, 𝑣𝑦) ⋅ 𝐸𝑜𝑏𝑗(𝑣𝑥, 𝑣𝑦)

Coherence and imagingFourier theory of coherent image formation

14

𝐼𝑖𝑚𝑎(𝑥′, 𝑦′) = 𝐴𝑝𝑠𝑓 𝑥, 𝑦 ∗ 𝐸𝑜𝑏𝑗 𝑥, 𝑦2

object

amplitude

U(x,y)

PSF

amplitude-

response

Hpsf (xp,yp)

image

amplitude

U'(x',y')

convolution

result

object

amplitude

spectrum

u(vx,vy)

coherent

transfer

function

hCTF (vx,vy)

image

amplitude

spectrum

u'(v'x,v'y)

product

result

Fourier

transform

Fourier

transform

Fourier

transform

Coherent Imaging

object

intensity

I(x,y)

squared PSF,

intensity-

response

Ipsf

(xp,y

p)

image

intensity

I'(x',y')

convolution

result

object

intensity

spectrum

I(vx,v

y)

optical

transfer

function

HOTF

(vx,v

y)

image

intensity

spectrum

I'(vx',v

y')

produkt

result

Fourier

transform

Fourier

transform

Fourier

transform

Incoherent Imaging

Coherence and imagingFourier theory of image formation

15

object

-0.05 0 0.05

0

0.1

0.2

0.3

0.4

0.5

0.6

0.7

0.8

0.9

1

incoherent coherent

-0.05 0 0.05

0

0.1

0.2

0.3

0.4

0.5

0.6

0.7

0.8

0.9

1

-0.05 0 0.05

0

0.1

0.2

0.3

0.4

0.5

0.6

0.7

0.8

0.9

1

-0.05 0 0.05

0

0.1

0.2

0.3

0.4

0.5

0.6

0.7

0.8

0.9

1

-0.05 0 0.05

0

0.1

0.2

0.3

0.4

0.5

0.6

0.7

0.8

0.9

1

-0.05 0 0.05

0

0.1

0.2

0.3

0.4

0.5

0.6

0.7

0.8

0.9

1

-0.05 0 0.05

0

0.1

0.2

0.3

0.4

0.5

0.6

0.7

0.8

0.9

1

-0.05 0 0.05

0

0.1

0.2

0.3

0.4

0.5

0.6

0.7

0.8

0.9

1

-0.05 0 0.05

0

0.1

0.2

0.3

0.4

0.5

0.6

0.7

0.8

0.9

1

-0.05 0 0.05

0

0.1

0.2

0.3

0.4

0.5

0.6

0.7

0.8

0.9

1

bars resolved bars not resolved bars resolved bars not resolved

Coherence and imagingComparison coherent – incoherent image formation

16

▪ Incoherent image:

homogeneous areas, good similarity between object

and image, high fidelity

▪ Coherent image:

Granulation of area ranges, diffraction ripple at

edges

incoherent coherent

incoherent

coherent

Coherence and imagingComparison coherent – incoherent image formation

17

𝐼 𝑥 =ම𝑒2𝜋𝑖𝜈𝑠(𝑥1−𝑥2) ⋅ 𝑆(𝜈𝑠)2 ⋅ ℎ 𝑥 − 𝑥1 ⋅ ℎ∗ 𝑥 − 𝑥2 ⋅ 𝑇 𝑥1 ⋅ 𝑇∗ 𝑥2 d𝑥1d𝑥2d𝜈𝑠

Coherence and imagingPartially coherent imaging – Köhler illumination

Simulation of partially coherent illumination:

▪ Finite size of light source

▪ Every point in light source is considered to emit independent (incoherent)

▪ Off-axis point in light source plane generates an inclined plane wave in the object

▪ Angular spectrum illumination of the object describes partial coherence

▪ Intensity in image plane:

object plane

pupilplane

imageplane

f f f f

u() U (x)1

h()

f f

lightsource

s() U (x)0

T(x)

s

s h(x)

I(x)

T(x)

18

Coherent

Off Axis Annular Annular

Dipole Rotated Dipole

Disk = 0.5 Disk = 0.8

6 -Channel

▪ Variation of the pupil illumination

▪ Enhancement of resolution

▪ Improvement of contrast

▪ Object specific optimization

Ref: W. Singer

Coherence and imagingPupil illumination pattern

19

𝑃(𝑥) = 𝐵(𝑥) ⋅ 𝑒𝑖Φ(𝑥)

𝐸(𝑥) = 1 + 𝑖 ⋅ Φ(𝑥)

𝐸′(𝑥′) = 𝑖𝑎 + 𝑖 ⋅ Φ(𝑥′)

𝐼′ 𝑥′ = 𝑎2 + 𝑎 ⋅ Φ(𝑥′)

condenserimage

Bertrand

lens

objective

lens

ring shaped

stopobject

phase

plate

▪ Pure phase object is not visible

▪ Approximation small phase

▪ Pupil modified: 0th order damped by factor a

and phase rotated by 90°

▪ Approximated image intensity

0th order

Phase imagingZernike phase contrast

20

▪ Phase contrast methods:

Making phase object visible

sample 1

bright

field

phase

contrast

image

sample 2 sample 3

Phase imagingComparison bright field vs. phase contrast

21

Possible options in Zemax:

▪ Convolution of image with PSF

1. geometrical

2. with diffraction

▪ Geometrical raytrace analysis

1. simple geometrical shapes (IMA-files)

2. bitmaps

▪ Diffraction imaging:

1. partially coherent

2. extendedwith variable PSF

▪ Structure of options in Zemax not clear

▪ Redundance

▪ Field definition and size scaling not good

▪ Numerical conditions and algorithms partially unclear

Imaging with ZEMAXOverview

22

Field size definitions

▪ Total field size in data (angle or length)

▪ Selected field index

▪ Relative size of structure in the total field

▪ Shown part of the field

▪ Not completely consistent

in the different imaging tools

plotted image size

/ pixel x Npix

selected field (index)

field heigth

relative field size

of object structure

y

real maximum size

of the field

x

Imaging with ZEMAXOverview

23

▪ Field height: size of object in the specific coordinates of the system

- zero padding included (not: size = diameter)

- image size shown is product of pixel number x pixel size

- can be full field or center of local extracted part of the field

▪ PSF-X/Y points: number of field points to incorporate the changes of the PSF,

interpolation between this

coarse grid

▪ Object: bitmap

▪ PSF: geometrical or diffraction

Imaging with ZEMAXImage simulation

24

25

object image

7x7 pixel IMA file10 000 raytraces

From random position inside object pixel

To random position in entrance pupil

Spot diagram

Ref.: M. Eßlinger

Imaging with ZEMAXGeometric image analysis

Geometrical imaging by raytrace

▪ Binary IMA-files with geometrical shapes

▪ Choice of:

- field size

- image size,

- wavelengths

- number of rays

▪ Interpolation possible

Imaging with ZEMAXGeometric image analysis

26

Geometrical imaging by raytrace

of bitmaps

▪ Extension of 1st option:

can be calculated at any surface

▪ If full field is used, this

corresponds to a footprint with

all rays

▪ Example: light distribution

in pupil, at last surface, in image

Imaging with ZEMAXGeometric image analysis

27

28

10 rays per pixel1 ray per pixel

100 rays per pixel 1000 rays per pixelRef.: M. Eßlinger

Imaging with ZEMAXGeometric bitmap image analysis

▪ Different types of partially coherent model algorithms possible

▪ Only IMA-Files can be used as objects

▪ a describes the coherence factor (relative pupil filling)

▪ Very limited source distributions

▪ Control and algorithms not clear

Imaging with ZEMAXPartially coherent image analysis

29

▪ Classical convolution of PSF

with pixels of IMA-File

▪ Coherent and incoherent

model possible

▪ PSF may vary over field

position

Imaging with ZEMAXExtended diffraction image analysis

30

31

Ref.: M. Eßlinger

▪ IMA (Image file)

- Illumination brightness in each point of the object

- Zemax provides basic shapes like the letter „F“

- ASCII format with 10 different grey values or binary with 256 grey values

▪ BIM (binary image)

- like IMA, but 64bit (double precision) float values

▪ ZBF (Zemax beam file)

- for sophisticated illumination optics

- many features only available in Premium Version of Zemax

▪ BMP (bmp, jpg or png)

- 3 x 8 bit RGB values ( raytrace with FdC: 656 nm, 587 nm and 486 nm)

- for greyscale detector: raytrace with FdC, averaging on detector plane

Imaging with ZEMAXImaging objects

32

Ref.: M. Eßlinger

Advantages and Disadvantages of Geometric Raytracing

+ Easy to understand

+ Field dependent errors are considered automatically

- Does not include Diffraction Limit

- Requires large number of rays (slow)

- Coherent imaging is difficult

ObjectFile type

conv. raytrace diffraction

spatial variant aberr.

pupilaberr.

Coherence

BMP IMA BIM ZBF coh.part. coh. incoh.

Image Simulation X X X

Geometric X X X X X

Geometric Bitmap X X X X X X

Partially Coherent X X X

Extended Diffraction X X X X

Imaging with ZEMAXSummary

33

Ref.: M. Eßlinger

Advantages and Disadvantages of Convolution based algorithms

+ Easy to implement Diffraction Limit

+ Fast Fourier Transform based (fast)

+ Possibility to calculate also coherent imaging

- Although diffraction is considered, aberrations are calculated from tracing

geometrical rays (result is not a rigorous wave-optical solution)

- FFT-PSF in systems with pupil-aberration creates wrong results ( Only

Huygens-PSF method works correctly )

- Field dependent errors and spatial variant aberrations

are not trivial to implement (possible with Zemax, but it‘s not always clear

how this is performed)

Imaging with ZEMAXSummary